We present a quantitative surface x-ray analysis of the buried Ni/Cu(001) interface structure after deposition of 3 and 5 monolayers of Ni at room temperature. Interface mixing is found where 27+/-10% of top layer Cu atoms are exchanged by Ni. Atomic scale simulations reveal a kinetic pathway for the Ni/Cu-exchange process and explain the observed limited degree of intermixing. A disperse distribution of Ni within the Cu surface with a preferential Ni-Ni separation of 3-4 nearest neighbor distances is determined.